Question

Plz. help ) An auto accelerates forward from 7.0 m/s at a uniform

Answer 1

Answer:

The auto is moving at 38.9 m/s

The auto took 45 seconds to travel the 1033 m

Explanation:

Constant Accelerated Motion

it's a type of motion in which the velocity of an object changes uniformly in time.

The relationship between initial and final speeds is calculated by the equation:

$v_f=v_o+at\qquad\qquad [1]$

Where a is the constant acceleration, vo the initial speed, vf the final speed, and t the time.

Another useful equation allows us to calculate the distance x traveled by the object:

$\displaystyle x=v_o.t+\frac{a.t^2}{2}\qquad\qquad [2]$

(a)

Solving [1] for t and substituting into [2] we find the equation:

$v_f^2=v_o^2+2ax$

This last equation will be used to solve the first part of the problem which gives the initial speed of vo=7 m/s, the uniform acceleration as a=0.71 m/s^2 and the distance traveled as x=1033 m, thus substituting:

$v_f^2=7^2+2(0.71)(1033)$

$v_f^2=49+1466.86=1515.86$

Thus:

$v_f=\sqrt{1515.86}=38.9$

$v_f=38.9 m/s$

The auto is moving at 38.9 m/s

(b)

To calculate the time, we solve [1] for t:

$\displaystyle t=\frac{v_f-v_o}{a}$

$\displaystyle t=\frac{38.9-7}{0.71}=45$

The auto took 45 seconds to travel the 1033 m